Path integral method for stochastic equations of financial engineering

The integral path method was applied to determine certain stochastic variables which occur in problems of financial engineering.  A stochastic variable was defined by a stochastic equation where drift and volatility are functions of a stochastic variable.  As a result, for transition probability density, a path integral was built by substituting variables Wiener's path integral (Wiener's measure).  For the stochastic equation, Ito rule was applied in order to interpret a stochastic integral.  The path integral for transition probability density was also found as a result of the Fokker--Planck equation solution, corresponding to the stochastic equation.  It was shown that these two approaches give equivalent results.

stochastic equation
Fokker--Plank equation
transition probability density
path integrals
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